What is minimized in the least squares method of adjusting observations?

In the least squares method, the primary goal is to find the best-fitting line or solution that minimizes the discrepancy between observed values and the values predicted by a model. This discrepancy is mathematically represented by the residuals, which are the differences between the observed data points and the estimated values.

By focusing on minimizing the sum of the squares of all residuals, the least squares method effectively reduces the effect of measurement errors and variations in the observed data. Squaring the residuals helps to emphasize larger errors more than smaller ones, providing a more robust solution that accounts for outliers and ensures that the overall fit of the model is as close as possible to the actual data. This minimization process leads to a unique solution that produces the best linear unbiased estimates of the parameters involved in the model.

The other options, while related to various aspects of data analysis, do not capture the essence of what is being minimized in the least squares approach. The focus on the residuals is what distinguishes this method and gives it its name. In summary, the least squares method's effectiveness hinges on the minimization of the sum of the squares of all residuals, which leads to an optimal fit for the observed data.